Abstract

We propose a flat lensing effect using a periodic loss-modulated material. In particular, we consider a two-dimensional square and rhombic arrangement of lossy cylinders embedded in a host media with the same refractive index. The effect is predicted by the dispersion curves obtained by a coupled mode expansion of Maxwell equations and by numerical beam propagation experiments. From both analytical and numerical studies, we show that, for a range of frequencies, light beams undergo negative diffraction on propagation through the loss-modulated medium, providing a window of high transmission. The phase shifts accumulated by negative diffraction within the structure are then compensated by normal diffraction, leading to substantial focalization beyond it.

© 2013 Optical Society of America

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  1. L. Jia and E. L. Thomas, “Two-pattern compound photonic crystals with a large complete photonic band gap,” Phys. Rev. A 84, 033810 (2011).
    [CrossRef]
  2. L. Jia and E. L. Thomas, “Theoretical study on photonic devices based on a commensurate two-pattern photonic crystal,” Opt. Lett. 36, 3416–3418 (2011).
    [CrossRef]
  3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
    [CrossRef]
  4. K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  5. D. Chigrin, S. Enoch, C. S. Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
    [CrossRef]
  6. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  7. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
    [CrossRef]
  8. A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
    [CrossRef]
  9. L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
    [CrossRef]
  10. E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
    [CrossRef]
  11. K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
    [CrossRef]
  12. K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
    [CrossRef]
  13. M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
    [CrossRef]
  14. N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
    [CrossRef]
  15. R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
    [CrossRef]
  16. M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).
  17. S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
    [CrossRef]
  18. M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
    [CrossRef]
  19. P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal–dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  20. D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
    [CrossRef]
  21. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  22. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  23. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  24. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
    [CrossRef]
  25. N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
    [CrossRef]
  26. H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
    [CrossRef]
  27. CrystalWave software by Photon Design Ltd., http://www.photond.com .

2012 (2)

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
[CrossRef]

2011 (2)

L. Jia and E. L. Thomas, “Two-pattern compound photonic crystals with a large complete photonic band gap,” Phys. Rev. A 84, 033810 (2011).
[CrossRef]

L. Jia and E. L. Thomas, “Theoretical study on photonic devices based on a commensurate two-pattern photonic crystal,” Opt. Lett. 36, 3416–3418 (2011).
[CrossRef]

2010 (3)

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

2009 (3)

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

2008 (2)

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

2006 (2)

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal–dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

2004 (1)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

2003 (4)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

D. Chigrin, S. Enoch, C. S. Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Akozbek, N.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Ambati, M.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

Belov, P. A.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal–dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Bloemer, M. J.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Botey, M.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).

Cakmak, A. O.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Cappeddu, M. G.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Centini, M.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Chigrin, D.

Christodoulides, D. N.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Cojocaru, C.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Colak, E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

D’Orazio, A.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

de Ceglia, D.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Durant, S.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Enoch, S.

Fang, N.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

Gertus, T.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal–dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Haus, J. W.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Herrero, R.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).

Jia, L.

L. Jia and E. L. Thomas, “Two-pattern compound photonic crystals with a large complete photonic band gap,” Phys. Rev. A 84, 033810 (2011).
[CrossRef]

L. Jia and E. L. Thomas, “Theoretical study on photonic devices based on a commensurate two-pattern photonic crystal,” Opt. Lett. 36, 3416–3418 (2011).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Kumar, N.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Ladisa, A.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

Lee, H.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

Loiko, Y.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Maigyte, L.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Ozbay, E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

Peckus, M.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Radziunas, M.

R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
[CrossRef]

M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

Rondinone, V.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

Sánchez-Morcillo, V. J.

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Scalora, M.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Serebryannikov, A. E.

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Sirutkaitis, V.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

Srituravanich, W.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

Staliunas, K.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

R. Herrero, M. Botey, M. Radziunas, and K. Staliunas, “Beam shaping in spatially modulated broad-area semiconductor amplifiers,” Opt. Lett. 37, 5253–5255 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).

Sun, C.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Tayeb, G.

Thomas, E. L.

L. Jia and E. L. Thomas, “Two-pattern compound photonic crystals with a large complete photonic band gap,” Phys. Rev. A 84, 033810 (2011).
[CrossRef]

L. Jia and E. L. Thomas, “Theoretical study on photonic devices based on a commensurate two-pattern photonic crystal,” Opt. Lett. 36, 3416–3418 (2011).
[CrossRef]

Thylen, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

Torres, C. S.

Trull, J.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vilaseca, R.

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

Vincenti, M. A.

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

Xiong, Y.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

Zhang, X.

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

Appl. Phys. Lett (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett 74, 1212–1214 (1999).
[CrossRef]

J. Appl. Phys. (1)

E. Colak, A. O. Cakmak, A. E. Serebryannikov, and E. Ozbay, “Spatial filtering using dielectric photonic crystals at beam-type excitation,” J. Appl. Phys. 108, 113106 (2010).
[CrossRef]

Nature (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef]

New J. Phys. (1)

H. Lee, Y. Xiong, N. Fang, W. Srituravanich, S. Durant, M. Ambati, C. Sun, and X. Zhang, “Realization of optical superlens imaging below the diffraction limit,” New J. Phys. 7, 255 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Photon. Nanostr. Fundam. Appl. (1)

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Phys. Rev. A (7)

M. A. Vincenti, D. de Ceglia, V. Rondinone, A. Ladisa, A. D’Orazio, M. J. Bloemer, and M. Scalora, “Loss compensation in metal–dielectric structures in negative-refraction and super-resolving regimes,” Phys. Rev. A 80, 053807 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain–loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain–loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

L. Jia and E. L. Thomas, “Two-pattern compound photonic crystals with a large complete photonic band gap,” Phys. Rev. A 84, 033810 (2011).
[CrossRef]

Phys. Rev. B (3)

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal–dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Phys. Rev. E (1)

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (2)

M. Radziunas, M. Botey, R. Herrero, and K. Staliunas, “Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers,” Appl. Phys. Lett (to be published).

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Figures (6)

Fig. 1.
Fig. 1.

Real spatial dispersion curves of the first three modes [real part of kz as a function of kx, where k⃗=(kx,kz)] in normalized q units, for (a) a/λ=0.76 and (b) a/λ=1.0, just below and above the M point lying at a/λ=0.83. (c), (d) Attenuation, imaginary part of kz as a function of kx, in normalized q units for the same modes. The curvature of the dispersion, for the least attenuated mode at kx=0, is shown depending on frequency (in normalized a/λ units) for propagation along the diagonal for 2θ=75°. The black dashed lines indicate the dispersion for homogenous propagation in (a) and (b) and the corresponding curvatures in (e). The first BZ (blue area) and the corresponding symmetry points are represented in (f).

Fig. 2.
Fig. 2.

Curvature of the dispersion, for the least attenuated mode at kx=0, is shown depending on frequency (in normalized a/λ units) for propagation along the diagonal (a) for 2θ=105° and (c) 2θ=90°. The black dashed lines in (a) and (c) denote the curvature of dispersion for homogenous propagation. (b), (c) Corresponding reciprocal lattice and symmetry points.

Fig. 3.
Fig. 3.

Beam propagation through the long diagonal of a LMM rhombic structure, made of lossy cylinders embedded in air, R=0.2a, where a is the direct lattice distance, a=2π/q. (a) Finite-difference time domain transmission map for cylinders with ncyl=1+0.4i; the vertical axis denotes the carrier frequency, in a/λ units, of the 1.5 μm wide incident Gaussian and the horizontal axis, the normalized distance from the sample. (b), (c) Transverse cross section at the output face of the device and at a distance of z=36a after the structure, denoted D1 and D2 in (a), where the continuous yellow curve is for comparison with propagation in free space.

Fig. 4.
Fig. 4.

(a) Curvature of the phase of the spatial Fourier transform of a Gaussian beam just exiting the LMM slab. (b), (c), (d) Comparison of the phase profile and the same phase profile for a beam propagating in free space (dotted curve), for a/λ=0.67, 0.81, and 0.97, respectively.

Fig. 5.
Fig. 5.

Beam propagation through the short diagonal of a LMM rhombic structure. (a) Transmission map at x/a=0 and (b), (c) transverse cross section at D1 and D2. (d) Phase curvature of the beam exiting after propagation through the LMM.

Fig. 6.
Fig. 6.

Beam propagation through the diagonal of a LMM square structure. (a) Transmission map at x/a=0. (b), (c) Transverse cross section at D1 and D2. (d) Phase curvature of the beam exiting after propagation through the LMM.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

2E⃗+n2ω2c2E⃗=0.
n(r⃗)=n0+2n1[cos(q⃗1,0·r⃗)+cos(q⃗0,1·r⃗)],
E=l,pAl,peik⃗l,pr⃗+c.c.,
l,p[2Al,p+2ik⃗l,p·⃗∇Al,pkl,p2+n2k02Al,p]eik⃗l,p·r⃗=0,
[k02(n02+4n12)k22k⃗l,p·k⃗kl,p2]Al,p+2n0n1k02(Al+1,p+Al1,p+Al,p+1+Al,p1)+n12k02(Al+2,p+Al2,p+Al,p+2+Al,p2)+2n12k02(Al+1,p+1+Al+1,p1+Al1,p+1+Al1,p1)=0.

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